Self-Relaxation for Multilayer Perceptron

We propose a way to show the inherent learning complexity for the multilayer perceptron. We display the solution space and the error surfaces on the input space of a single neuron with two inputs. The evolution of its weights will follow one of the two error surfaces. We observe that when we use the back-propagation(BP) learning algorithm (1), the wight cam not jump to the lower error surface due to the implicit continuity constraint on the changes of weight. The self-relaxation approach is to explicity find out the best combination of all neurons' two error surfaces. The time complexity of training a multilayer perceptron by self-relaxationis exponential to the number of neurons.